Field of the Invention
The invention relates to a method of proximity correction for E-beam lithography.
In the technique of electron beam lithography an electron beam is used to delineate the features of a semiconductor device by selectively irradiating a substrate coated with an electron-beam sensitive resist. The electron beam is deflected and shaped in a precise manner to define the required shape in the resist. The pattern is then developed in the resist. The substrate can be either a semiconductor wafer, as in the case of direct-write lithography, or glass, metal or other material as in the case of a high resolution mask for subsequent use in fabricating the semiconductor device.
When an electron beam penetrates a material, such as the electron-beam sensitive resist or the substrate, the electrons in the beam collide with molecules in the material and are scattered in all directions from the resist and the substrate. The electrons are scattered both in the forward direction, mainly from the resist, and laterally and in the backward direction, mainly from the substrate. The scattering causes regions of the resist nearby to directly exposed regions to be additionally exposed to scattered electrons. This has the effect of reducing the resolution of the technique. The electrons which are back-scattered from the substrate affect a larger area of the resist than the electrons which are forward scattered from the resist. The spreading of the electron beam due to the backscattered electrons is usually characterized by a parameter .beta., the backscatter range, which is of the order of 2 .mu.m to 10 .mu.m. The spreading of the electron beam due to the combined effect of the forward scattering, beam defocussing and aberrations is usually characterized by a parameter .alpha. which is of the order of 0.1 .mu.m.
When two regions to be directly exposed are positioned close together, each receives not only the direct electron beam exposure during irradiation of that region, which will hereinafter be referred to as "the incident dose", but also an extra exposure due to the lateral scattering of electrons while directly exposing the adjacent regions. Consequently, closely spaced regions become more heavily exposed from the same incident dose than isolated regions. The resist in the gap between the two closely spaced shapes will receive exposure from the scattered electrons of both shapes. The effect of this is to narrow the gap between the shapes.
This phenomenon is referred to as the "proximity effect". In the manufacturing of VLSI masks and/or chips by E-Beam lithography it causes deformations of the developed shapes and is a major problem, particularly when the smallest gap or shape size is less than 1 .mu.m.
Many techniques have been used which try to eliminate or reduce the proximity effect including varying the energy of the electron beam, the region of the E-Beam application, the materials of the substrate and the resist and using multi-layer resists.
A first main way of correcting for the proximity effect is to modify the E-Beam incident "dose" applied at each point of the resist, without modifying the design shapes, in a way which takes into account the layout of the chip/mask image that is required. The calculation of the modification to the E-beam dose required at each point is non-trivial and cannot be performed exactly without compromising some additional technical requirements, such as nonnegativity of the off-shape dose and stability of the solution for the incident dose.
One scheme for eliminating the proximity effect in this way is called GHOST and is described in J. Appl. Phys. 54(6), pp. 3673-3681, (1983) and EP-A-97 417 of Owen and Rissman. This scheme uses an approach of "equalizing the off-shape exposure". In this scheme, in addition to an on-shape dose, off-shape points are also directly exposed with a dose to compensate for the uneven exposure by the back-scattered electrons. The resist therefore receives a constant offset background exposure at all off-shape points over its entire surface and the resulting pattern is undistorted. This, however, has the disadvantages of lower contrast and lower throughput because of the off-shape exposure.
Another approach to proximity correction are what could be termed exposure equalization" methods. In "exposure equalization" methods the values of the incident dose over the surface of the resist are modified so as to achieve equal exposure values at all on-shape points.
A particular method of "exposure equalization" type, the so-called self-consistent technique, is described in J. Vac. Sci. Tech. 15, p. 931, (1978) and in IBM J. Res. Develop. 24 pp. 438-451, (1980). The designed set of shapes is first divided into a set of subshapes, which are sufficiently small that it can be assumed that the correction factor is constant across each subshape. The requirement of the self-consistent technique is that the average exposure be equal for all subshapes. This leads to a fully determined system of linear equations for the correction factors. This method is capable of producing excellent results. However, it has the problem that the linear system of equations is usually ill-conditioned, especially for large numbers of subshapes. This results in highly unstable solutions, which are very dependent on the precision of the input parameters and prone to large errors. Another disadvantage of this technique is its prohibitively high computational load, especially for submicron technologies and/or for high accelerating voltages.
A further method of the "exposure equalization" type has been described in EP-A-166 549 of Pavkovich and in J. Vac. Sci. Tech. B 4(1), pp. 159-163, (1986) by Pavkovich. The method uses an approximate solution of the basic integral equation, which describes the requirement of equal on-shape exposure. This method overcomes a problem of the high computational load of the self-consistent technique by using a coarse grid for a solution.
However, the exposure equalization methods, in general, are sensitive to process tolerances, and require a lot of trial and error to arrive at starting parameters that give acceptable results. Basic parameters, such as the development time, generally depend on the chip/mask image density, so that each design usually requires individual processing and development adjustments.
Another problem associated with methods of the exposure equalization type is that attempts to account for a finite value of the spreading of the electron beam due to the forward scattering, characterized by the parameter .alpha., lead to ill-posed problems. This results in highly oscillatory incident doses, which could even have unrealizable negative solutions for the incident dose.
In another group of methods of this type, for example those published in J. Vac. Sci. Technol. B 4(1), pp. 168-175, (1986) by Haslam and McDonald and in J. Vac. Sci. Technol, B 6(1), pp. 432-435 by Gerber, attempts were made to choose the incident dose so that the exposure be constant on-shape and zero off-shape. Since the exposure cannot be zero off-shape, due to the backscatter, these techniques obtain unphysical negative incident off-shape doses by solving the corresponding integral equations. The truncation of the dose value at zero leads to further uncontrollable image distortions.
An important improvement to the self-consistent technique was first described in a paper by Berkowitz, Cook, Kwiatkowski and Goodreau, "Edge-Controlled, Self-Consistent Proximity Effect Corrections," pp. 125-142 in Semiconductor Processing ASTM STP 850, edited by D. C. Gupta, American Society for Testing and Materials (publisher), 1984. In this method the self-consistent technique is extended so that the average exposure over each exterior edge of a subshape is equal to the critical exposure value, hereinafter referred to as the "threshold value", such that edges are developed just to the desired location.
A further development of this method has been published in J. Vac. Sci. Technol. B 6(1), pp. 443-447, (1988) by Otto and Griffith. In this paper the test points are defined for each subshape. For edge subshapes the test points are chosen on their edges and the exposure at these test points is constrained to be threshold value. For interior subshapes the test points are chosen in their centres and the exposure there is specified at some value above the threshold. The system of linear equations which has to be solved is analogous to that of the self-consistent method. Although providing better pattern accuracy, this method suffers from all the other disadvantages of the self-consistent technique, in particular it requires unacceptably long CPU times.
The second main way of correcting for the proximity effect modifies the zone of application of the incident dose so as to provide a correct size of the final developed pattern.
One example of this is the scheme disclosed in EP-A-110 042 of F. Jones. In this scheme the constant dose is applied within contracted areas of each subshape, including edge and interior subshapes. The contraction is performed by decreasing all sides of a subshape by a constant distance, hereinafter referred to as the "bias". The method lacks the flexibility of a correction by a dose value modification, hence it is generally impossible to obtain high quality lithographic patterns with this method.
It is clear that the combination of the two aforementioned main ways of proximity correction could provide further improvement of pattern fidelity and/or further reduction in lithography sizes in the submicron range. It is common practice to apply a "bias" to the desired shapes, that is to expose smaller shapes than in the original design in order to account for various factors in the VLSI fabrication process that lead to the shape enlargement. For example, due to certain optical phenomena in the lithography process, the final VLSI pattern could enlarge, compared with its mask. Therefore the mask, which is fabricated by the E-beam lithography, has to be slightly contracted. On top of all biases dictated by the fab process in the art of E-beam lithography it is customary to apply an extra "bias" to the desired shapes, in order to account for shape enlargement due to the proximity effect and the resist dissolution in the lateral direction during the development process.
In the paper in J. Vac. Sci. Technol. B 3(1), pp. 148-152, (1985) by Chen, Neureuther and Pavkovich an attempt was described of equalizing the development bias for fabrication of long isolated lines of different widths. However, the scheme is only a rough approximation for a particular case and has not evolved into a generic approach, since the bias was not expressed in terms of the correct parameters.
Prior art proximity correction methods have all proved insufficient for E-beam lithography in manufacturing VLSI patterns with design rules in the submicron range.
It is, therefore, the object of this invention to provide a systematic method for correcting the proximity effect, which method is suitable for use in a manufacturing environment.
Therefore, in accordance with the present invention there is provided a method of proximity correction in an E-beam lithography system for exposing, on a E-beam sensitive resist, a design comprising at least one design shape, the method comprising determining the E-beam dose required at any given point of the design such that, on development, a shape control requirement is satisfied, wherein the determination of the E-beam dose is made in accordance with a predetermined relationship between an indicator and the required E-beam dose, the indicator being indicative of the degree of the proximity effect any point on the design, is such that at points not on a design shape the dose is constrained to be zero, and comprises the step of calculating the solution, at least at a plurality of points on the design, of an integral equation relating the indicator to the E-beam dose distribution.
Generally the amount of shape widening at a straight edge depends on the incident dose and the backscatter just around the edges of the shape, but not on the size of the shape. This is true as long as the shape is not too small so that the effect of the forward scattering is significant and has to be taken into account.
If dose values can be determined that give equal shape widening for all the design shapes, then using that shape-widening as the bias or etch parameter for contraction of design shapes prior to their exposure would assure that the final edge locations are correct. This requirement will be henceforth referred to as "the etch equalization" principle.
Therefore in a preferred form of the invention the method comprises the prior step of contracting each design shape by a predetermined bias to form a contracted design shape and the shape control requirement is that each contracted design shape be enlarged, on development, by the value of the predetermined bias.
The shape contraction or "pre-etching" is done as part of postprocessing. Usually post-processors use one single etch value that is applied to all shapes.
The method of the invention enables proximity correction to be performed which results in an accurate chip/mask image and at the same time allows relatively "loose" tolerances in the parameters for the lithography process and a gain in the E-beam tool throughput. These loose tolerances for the operating parameters and the increase in computational efficiency make the method particularly suitable for use in a manufacturing environment.
Preferably the determination of the E-beam dose comprises combining the values of the indicator at ones of the plurality of points. This allows values of the required dose to be found by interpolation of the indicator for locations on the design intermediate those at which the integral equation is solved.
The indicator can be any function that is indicative of the degree or magnitude of the proximity effect. Preferably the indicator is the electron backscatter, however the indicator can also be any other function of the backscatter such as a dose boost function which, at any given point of the design gives the value of the dose such that a shape edge at that point would, on development, have the correct locations. In this case the predetermined relationship between the indicator and the required dose is that the required E-beam dose is equal to the indicator for points which lie on a contracted design shape.
In the case where the indicator is the electron backscatter the predetermined relationship can be predetermined by determining, for the E-beam lithography system and a predetermined value of the bias, a relationship between the backscatter at a point on the edge of a design shape and the E-beam dose required at that point such that the edge of the design shape be moved, on development, by the value of the bias.
The dependence of the shape widening on the incident dose and the background backscatter can be determined either by an experimental calibration of a particular lithography system or by computer modelling of the development process.
The incident dose D required to obtain equal shape widening at all the shape edges depends on the background backscatter S. Hence an operational curve, D=f(S), can be deduced from the dependence of the shape widening on the incident dose for a given ETCH value of the shape widening. This operational curve D=f(S) will henceforth be referred to as a D-S diagram.
The D-S diagram can be applied as an operational curve for all on-shape points. Since the background scatter S is in turn defined by the incident dose distribution, namely it equals the convolution of the backscatter kernel B(x,y) with the dose distribution D(x,y), the final dose distribution satisfies the integral equation, which has to be solved prior to the final dose assignment.
Certain thin and/or high contrast resists, such as the imaging layer in a multi-layer resist, are well described by a "threshold model", at least for technology ground-rules that are wider than 3.alpha.. According to the threshold model all resist points where the exposure is above the threshold value are fully dissolved by a developer, and at all other points of the resist some residual thickness remains after development. In this case the incident dose values can be assigned so as to provide equal exposure values at all the shape edges. That single edge exposure value is equal to the threshold value. With that requirement satisfied, the exposure has a sharp front across any shape edge, the edge point being the point of the maximal slope. Since normally the forward scatter is characterized by a narrow symmetric kernel the exposure front is also symmetric with respect to the threshold level. This requirement will be henceforth referred to as "the exposure symmetrization" principle. In this form of the invention the predetermined relationship, between the backscatter and the required dose, is represented by the equation D=2t-2S, where D is the required dose, S is the backscatter and t is a threshold dose wherein if the dose applied to a point on the resist is greater than the threshold dose the resist is completely dissolved, on development, at that point.
For inner points of each shape, whose distance from the shape edge is greater than a couple of .alpha., the required incident dose can be smaller than the dose that is given by the D-S diagram, without significantly affecting the final edge location. In order to decrease the background backscatter it is advantageous to use incident dose values at these points which are as small as possible.
In accordance with this, the invention provides an option, that the requirement of equal widening be applied only to the external sleeves while for inner points an additional requirement holds. This is that the dose at inner points has to be chosen so as to assure that all the thickness of the resist will be dissolved, with some safety factor of overdosing. Therefore, two different D-S diagrams can be used for the external sleeves and for inner points.
Therefore in a preferred form of the invention the method further comprises the step of partitioning, prior to determination of the required dose, the shapes of the design into edge regions and internal regions each internal region being completely surrounded by an edge region, and wherein the E-beam dose for points in the internal regions is determined with the additional constraint that on development all the resist at that point be dissolved.
The incident dose for small shapes, i.e. whose dimension is 5.alpha. or less, can be additionally boosted in order to correct for the combined effect of forward scattering and beam divergence. The correction factor or .alpha.-boost factor, depends mainly on a shape size and also slightly on the backscatter S. The dependence of .alpha.-boost is registered either in a calibration experiment or by computer modelling of the lithography process. In a further preferred form of the invention the step of determining the required dose comprises multiplying the dose by a correction factor, the correction factor substantially correcting for the shape distortion due to the forward scattering of the electrons from the resist.
Since the invention involves solving an integral equation for an indicator function, such as the backscatter, which only varies slowly across the design, the solution of the integral equation can be performed on a very coarse grid, coarser than the design shapes themselves i.e. typically about 1 .mu.m for a 25 KeV machine.
Therefore in a preferred form of the invention the plurality of points, at which the integral equation is solved, are arranged on a cartesian grid, the spacing of the grid points being greater than the smallest linear dimension of the smallest design shape. The use of a relatively coarse grid greatly increases the speed and the computational efficiency of the method.
The invention further provides a process for E-beam lithography comprising the above proximity correction method and a method for manufacturing an integrated circuit comprising the E-beam lithography process.
In accordance with another aspect of the invention there is provided a proximity correction system for an E-beam lithography system wherein a design comprising at least one design shape is exposed on an E-beam sensitive resist, the system comprising means for contracting each design shape by a predetermined bias to form a contracted design shape and logic for determining the E-beam dose required at any given point of the design such that each contracted design shapes is enlarged, on development, by the value of the predetermined bias, and wherein the determination of the required E-beam dose is made in accordance with a predetermined relationship between an indicator and the required E-beam dose, the indicator being indicative of the degree of the proximity effect at any point on the design, the required E-beam dose is constrained to be zero at points not on a design shape and the determining logic comprises logic for calculating the solution, at the plurality of points on the design, of an integral equation relating the indicator to the E-beam dose distribution.